If you're a BFP (and by possession you also mean title), you would be subject to any lien/mortgage on the property. You can sue for damages in this context, in which case I'd assume it would be up to the court to determine the appropriate amount. Normally a breach of a covenant would just result in the possibility of rescission, but damages is still an option.

Same would be true if there was a lease on the property. Also if there was an easement or some other use right held by a third party.